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  • Open Access

A survey of dynamical complexity in a mean-field nonlinear model of human EEG

  • 1,
  • 2,
  • 3,
  • 1 and
BMC Neuroscience200910 (Suppl 1) :P285

https://doi.org/10.1186/1471-2202-10-S1-P285

  • Published:

Keywords

  • Salient Feature
  • Complex Behavior
  • Spectral Power
  • Neuronal Population
  • Dynamical Complexity
A recently proposed mean-field mesoscopic theory of mammalian cortex dynamics describes the salient features of rhytmic electrical activity in the cerebral macrocolumn, with the use of inhibitory and excitatory neuronal populations [1]. This model is capable of producing a range of important human EEG (electroencephalogram) features such as the alpha rhythm, the 40 Hz activity thought to be associated with conscious awareness [2] and the changes in EEG spectral power associated with general anesthetic effect (e.g. the so-called "biphasic" response) [3]. From the point of view of nonlinear dynamics, the model entails a vast parameter space within which multistability, pseudoperiodic regimes, different routes to chaos, fat fractals and resonances occur for a range of physiologically relevant parameter values, giving rise to a multitude of rich and elaborate bifurcation scenarios. Examples of these are the Shilnikov saddle-node bifurcation (see Figure 1 and [4]), the homoclinic doubling cascade and different kinds of resonances. The origin and the character of these complex behaviors and their relevance for EEG activity are illustrated.
Figure 1
Figure 1

The largest Lyapunov exponent in color reproduced from [4], with superimposed two-parameter continuation of saddle-node and period-doubling bifurcations for periodic orbits of a mesoscopic mean field EEG model. The leftmost wedge of chaos terminates for negative values of the exterior forcings p ee and p ei .

Authors’ Affiliations

(1)
Brain Sciences Institute (BSI), Swinburne University of Technology, P.O. Box 218, Victoria, 3122, Australia
(2)
Department of Mathematics and Statistics, Faculty of Arts and Sciences, Concordia University, 1455 de Maisonneuve Blvd. W., H3G 1M8 Montreal, Quebec, Canada
(3)
Donders Institute for Brain, Cognition and Behaviour, Centre for Neuroscience, Radboud University Nijmegen (Medical Centre), P.O. Box 9101//126, 6500, HB, Nijmegen, The Netherlands

References

  1. Liley DTJ, Cadusch PJ, Dafilis MP: A spatially continuous mean field theory of electrocortical activity. Network: Comput Neural Syst. 2002, 13: 67-113. 10.1088/0954-898X/13/1/303.View ArticleGoogle Scholar
  2. Bojak I, Liley DTJ: Self-organized 40 Hz synchronization in a physiological theory of EEG. Neurocomp. 2007, 70: 2085-2090. 10.1016/j.neucom.2006.10.087.View ArticleGoogle Scholar
  3. Bojak I, Liley DTJ: Modeling the effects of anesthesia on the electroencephalogram. Phys Rev E. 2005, 71: 041902(1–22)Google Scholar
  4. van Veen L, Liley DTJ: Chaos via Shilnikov's saddle-node bifurcation in a theory of the electroencephalogram. Phys Rev Lett. 2006, 97: 208101(1–4)Google Scholar

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